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A long-standing open problem in fault-tolerant quantum computation has beento find a universal set of transversal gates. As three of us proved in arXiv:0706.1382, such a set does not exist for binary stabilizer codes. Here wegeneralize our work to show that for subsystem stabilizer codes in $d$dimensional Hilbert space, such a universal set of transversal gates cannotexist for even one encoded qudit, for any dimension $d$, prime or nonprime.This result strongly supports the idea that other primitives, such as quantumteleportation, are necessary for universal fault-tolerant quantum computation,and may be an important factor for fault tolerance noise thresholds.

Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit